Find the roots of the following quadratic equations by factorisation:
$\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0$

Given:

Given quadratic equation is $\sqrt{2}x^2+7x+5\sqrt2=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$\sqrt{2}x^2+7x+5\sqrt2=0$

To factorise $\sqrt{2}x^2+7x+5\sqrt2=0$, we have to find two numbers $m$ and $n$ such that $m+n=7$ and $mn=\sqrt{2}\times(5\sqrt{2})=5(\sqrt2)^2=10$.

If $m=5$ and $n=2$, $m+n=5+2=7$ and $mn=(5)2=10$.

$\sqrt{2}x^2+5x+2x+5\sqrt2=0$

$\sqrt{2}x(x+\sqrt2)+5(x+\sqrt2)=0$

$(\sqrt{2}x+5)(x+\sqrt2)=0$

$\sqrt{2}x+5=0$ or $x+\sqrt2=0$

$\sqrt{2}x=-5$ or $x=-\sqrt2$

$x=-\frac{5}{\sqrt2}$ or $x=-\sqrt2$

The values of $x$ are $-\frac{5}{\sqrt2}$ and $-\sqrt2$.  

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Updated on: 10-Oct-2022

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